The common minimal common neighborhood dominating signed graphsP. SivaReddyDept. of Mathematics, Acharya Institute of Technology, Bangalore-560 090, India.authorK. R.RajannaProfessor and Head
Dept. of Mathematics
Acharya Institute of Technology
Bangalore-560 090
IndiaauthorKavitaPermiAssistant Professor
Dept.of Mathematics
Acharya Institute of Technology
Bangalore-560 090
India.authortextarticle2013eng‎In this paper‎, ‎we define the common minimal common neighborhood‎ ‎dominating signed graph (or common minimal $CN$-dominating signed‎ ‎graph) of a given signed graph and offer a structural‎ ‎characterization of common minimal $CN$-dominating signed graphs‎. ‎In the sequel‎, ‎we also obtained switching equivalence‎
‎characterization‎: ‎$\overline{\Sigma} \sim CMCN(\Sigma)$‎, ‎where‎ ‎$\overline{\Sigma}$ and $CMCN(\Sigma)$ are complementary signed‎ ‎graph and common minimal $CN$-signed graph of $\Sigma$‎ ‎respectively‎.Transactions on CombinatoricsUniversity of Isfahan2251-86572

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201318http://toc.ui.ac.ir/article_2640_a723658d1a823e061445180f458832f4.pdfdx.doi.org/10.22108/toc.2013.2640Bounding the domination number of a tree in terms of its annihilation numberNasrinDehgardaiAzarbaijan Shahid Madani UniversityauthorSepidehNorouzianAzarbaijan Shahid Madani UniversityauthorSeyed MahmoudSheikholeslamiAzarbaijan University of Tarbiat Moallemauthortextarticle2013engA set $S$ of vertices in a graph $G$ is a dominating set if every‎ ‎vertex of $V-S$ is adjacent to some vertex in $S$‎. ‎The domination‎ ‎number $\gamma(G)$ is the minimum cardinality of a dominating set‎ ‎in $G$‎. ‎The annihilation number $a(G)$ is the largest integer $k$‎ ‎such that the sum of the first $k$ terms of the non-decreasing‎ ‎degree sequence of $G$ is at most the number of edges in $G$‎. ‎In‎ ‎this paper‎, ‎we show that for any tree $T$ of order $n\ge 2$‎, ‎$\gamma(T)\le \frac{3a(T)+2}{4}$‎, ‎and we characterize the trees‎ ‎achieving this bound‎.Transactions on CombinatoricsUniversity of Isfahan2251-86572

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2013916http://toc.ui.ac.ir/article_2652_424dc767de5dc6d68475c6d0b1d46b2e.pdfdx.doi.org/10.22108/toc.2013.2652Gray isometries for finite $p$-groupsRezaSobhaniauthortextarticle2013eng‎We construct two classes of Gray maps‎, ‎called type-I Gray map and‎ ‎type-II Gray map‎, ‎for a finite $p$-group $G$‎. ‎Type-I Gray maps are‎ ‎constructed based on the existence of a Gray map for a maximal‎ ‎subgroup $H$ of $G$‎. ‎When $G$ is a semidirect product of two‎ ‎finite $p$-groups $H$ and $K$‎, ‎both $H$ and $K$ admit Gray maps‎ ‎and the corresponding homomorphism $\psi:H\longrightarrow {\rm‎ ‎Aut}(K)$ is compatible with the Gray map of $K$ in a sense which‎ ‎we will explain‎, ‎we construct type-II Gray maps for $G$‎. ‎Finally‎, ‎we consider group codes over the dihedral group $D_8$ of order 8‎ ‎given by the set of their generators‎, ‎and derive a representation‎ ‎and an encoding procedure for such codes‎.Transactions on CombinatoricsUniversity of Isfahan2251-86572

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20131726http://toc.ui.ac.ir/article_2762_9284f3f283a59b2d3778fed1f1d9bbfd.pdfdx.doi.org/10.22108/toc.2013.2762New skew Laplacian energy of simple digraphsQingqiongCaiCenter for Combinatorics, nankai University, Tianjin, ChinaauthorXueliangLiCenter for Combinatorics, Nankai University, Tianjin 300071, ChinaauthorJiangliSongCenter for Combinatorics, Nankai University, Tianjin, Chinaauthortextarticle2013engFor a simple digraph $G$ of order $n$ with vertex set‎ ‎$\{v_1,v_2,\ldots‎, ‎v_n\}$‎, ‎let $d_i^+$ and $d_i^-$ denote the‎ ‎out-degree and in-degree of a vertex $v_i$ in $G$‎, ‎respectively‎. ‎Let‎ $D^+(G)=diag(d_1^+,d_2^+,\ldots,d_n^+)$ and‎ ‎$D^-(G)=diag(d_1^-,d_2^-,\ldots,d_n^-)$‎. ‎In this paper we introduce‎ ‎$\widetilde{SL}(G)=\widetilde{D}(G)-S(G)$ to be a new kind of skew‎ ‎Laplacian matrix of $G$‎, ‎where $\widetilde{D}(G)=D^+(G)-D^-(G)$ and‎ ‎$S(G)$ is the skew-adjacency matrix of $G$‎, ‎and from which we define‎ ‎the skew Laplacian energy $SLE(G)$ of $G$ as the sum of the norms of‎ ‎all the eigenvalues of $\widetilde{SL}(G)$‎. ‎Some lower and upper‎ ‎bounds of the new skew Laplacian energy are derived and the digraphs‎ ‎attaining these bounds are also determined‎.Transactions on CombinatoricsUniversity of Isfahan2251-86572

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20132737http://toc.ui.ac.ir/article_2833_dc29c895a9ecdf11e850c68593ab72de.pdfdx.doi.org/10.22108/toc.2013.2833A comprehensive survey: Applications of multi-objective particle swarm optimization (MOPSO) algorithmSoniyaLalwaniStatistician, R & D, Advanced Bioinformatics Centre, Birla Institute of Scientific Research, Jaipur
PhD student, Department of Mathematics, Malaviya National Institute of Technology, JaipurauthorSorabhSinghalProject student, R & D, Advanced Bioinformatics Centre, Birla Institute of Scientific Research, JaipurauthorRajeshKumarAssociate Professor, Department of Electrical Engineering, Malaviya National Institute of Technology, JaipurauthorNilamaGuptaAssociate Professor, Department of Mathematics, Malaviya National Institute of Technology, Jaipurauthortextarticle2013engNumerous problems encountered in real life cannot be actually formulated as a single objective problem; hence the requirement of Multi-Objective Optimization (MOO) had arisen several years ago. Due to the complexities in such type of problems powerful heuristic techniques were needed, which has been strongly satisfied by Swarm Intelligence (SI) techniques. Particle Swarm Optimization (PSO) has been established in 1995 and became a very mature and most popular domain in SI. Multi-Objective PSO (MOPSO) established in 1999, has become an emerging field for solving MOOs with a large number of extensive literature, software, variants, codes and applications. This paper reviews all the applications of MOPSO in miscellaneous areas followed by the study on MOPSO variants in our next publication. An introduction to the key concepts in MOO is followed by the main body of review containing survey of existing work, organized by application area along with their multiple objectives, variants and further categorized variants.Transactions on CombinatoricsUniversity of Isfahan2251-86572